Download 5-1 Ax + By = C and intercepts

Warm up Problems
1. Solve the following equation for y:
2x + 3 y = 9
2. Graph y = − 2 x + 3 using the slope and y-
3
intercept.
3. What is the y-intercept of the line in 2.?
5.1 Equations of the form
Ax + By = C
The equation Ax + By = C where A, B and C
are numbers is also a linear equation. It is
called a General Linear Equation.
Examples:
2x −3 y = 6
3x + 5 y =10
Graphing lines in
Ax + By = C form
Method 1: Graph using the intercepts.
Recall:
• The x-intercept is the point (a,0) where the
line crosses the x-axis.
• The y-intercept is the point (0,b) where the
line crosses the y-axis.
To find the x-intercept, we set y = 0 and solve.
To find the y-intercept, we set x = 0 and solve.
Examples:
1. Given 5x − 2 y =10
a. Find the x-intercept
b. Find the y-intercept
c. Sketch the graph of the equation
y
x
Do: Given 4x − 5 y = 20
a. Find the x-intercept
b. Find the y-intercept
c. Graph the equation
x
y
Method 2: Writing the line in
y = mx + b form
Examples:
1. Given 5x − 2 y =10
a. Find the slope and y-intercept
b. Graph the line
Do. Given 4x − 5 y − 20 = 0
a. Find the slope and y-intercept
b. Graph the line
Before we can use the y-intercept
and slope to graph a linear equation,
we must write the equation as
y=mx + b
Special Cases
Find the slope and the y-intercept and graph
1. 4x − 6 y = 0
2.
y+ 5 = 0